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Given the diagram, a supplement to

Given the diagram, a supplement to-example-1
User Mcfedr
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1 Answer

5 votes

Given:

The figure of a quadrilateral ABCD.

To find:

The supplement of angle ABC.

Solution:

We know that, two angles are called supplementary angles if their sum is 180 degrees.


\angle ABC+\angle BAC=110^\circ+40^\circ


\angle ABC+\angle BAC=150^\circ\\eq 180^\circ

So,
\angle BAC is not a supplement of
\angle ABC.


\angle ABC+\angle ADC=110^\circ+90^\circ


\angle ABC+\angle ADC=200^\circ

So,
\angle ADC is not a supplement of
\angle ABC.


\angle ABC+\angle DAB=110^\circ+(40+30)^\circ


\angle ABC+\angle DAB=110^\circ+70^\circ


\angle ABC+\angle DAB=180^\circ

So,
\angle DAB is a supplement of
\angle ABC.

In the same way
\angle ABC+\angle BDC\\eq 180^\circ.

So,
\angle BDC is not a supplement of
\angle ABC.

Therefore, the correct option is C.

User Milia
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8.1k points